While Azza M. Al-Derby points you to a variant for staining cells in sputum (1963, staining with Ehrlich's haematoxylin and counterstaining with carbol-chromotrope 2R) I would like to remind you of original sources for Wright(-Giemsa) staining and some possibilities for reading protocols (cf.also enclosed pdf).
Not knowing which specific type of cells you want to localize with your , I would like to point you also to Lemière et al, 2001: Comparison of cellular composition of induced sputum analyzed with Wright staining and immunocytochemistry, Journal of Allergy and Clinical Immunology108, No 4, Oct2001, Pages 521–523: stating “Agreement between Wright staining and immunocytochemistry was poor for lymphocytes and epithelial cells”.
But protocols of how to apply and use Wright(-Giemsa) Stains one can find explicitely in (technical) data sheets of suppliers/companies like (number of suppliers not exhaustive, DISCLAIMER: no affiliation to any mentioned company,no financial interests, no recommendations):
MERCK ( http://www.vitus.by/userfiles/file/Products_MERCK/Microscopy.pdf ) Wright's eosin-methylene blue blood smears:Dye mixture for microscopy 25 g Product No: 1.09278; 0.24 g Wright's eosin-methylene blue in 100 ml methanol; leave to stand for 5 days and filter.
Other stains come into mind:, e.g. Tetrachrome stain, certified (MacNeal) [Blood stain similar to Wright’s stain. Also useful for staining bone sections.], cf.http://www.polysciences.com/Catalog/Department/Product/98/categoryid--66/pageindex--1/productid--262/
having soome troubles with automatic info-forwarding for new answers and replies via Researchgate I found your answer just recently when joining RG for today. In answer to your questions, - and not to use much space in the answering form - I add here a pdf containing information you perhaps might have no access via Internet.
Prepare always fresh specimen- Peripheral smears from a freshly drawn blood specimen (EDTA purple top tubes). Allow smears to air dry completely before staining.Please mix the Wright Stain and buffer mixture before blood smears are
made or before the smears are air drying. Combine 15ml of Wright Stain with 75ml of Wright Stain Buffer, mix well and allow to stand for at least 10 minutes. Make sure that a metallic sheen is observed on the surface before staining, Place freshly prepared and air dried blood smears in a manual staining rack -->Place slide rack with air dried blood smears in Methanol for 30 seconds---> (Adjust timer for 30 seconds--> Take a disposable pipette and flood the Wright Stain on the
appropriately labeled slides. Set timer for 3 minutes. Place oxidizing Wright Stain and Wright Stain Buffer Mixture on Wright stained slides laying on slide rack (Displacing the Wright .Stain off the slides with the pipette filled with Wright Stain/buffer mixture and viewing a metallic sheen on the top of slides.Set timer for 6 minutes. Place slides in Wright Stain Buffer for 1.5 minutes. Set timer for 1.5 minutes. Retrieve slide rack with stained slides from buffer rinse and allow to air dry before examination with immersion oil and 100X objective.Wipe excess stain from back of slides with methanol soaked gauze, being careful not to wipe off the stained side of the
slides.Place on slide envelope or slide flat/folder and proceed to the microscope room. Place 1 drop of immersion oil onto slide to be viewed making sure